Tough double-bouligand architected concrete enabled by robotic additive manufacturing

Nature has developed numerous design motifs by arranging modest materials into complex architectures. The damage-tolerant, double-bouligand architecture found in the coelacanth fish scale is comprised of collagen fibrils helically arranged in a bilayer manner. Here, we exploit the toughening mechanisms of double-bouligand designs by engineering architected concrete using a large-scale two-component robotic additive manufacturing process. The process enables intricate fabrication of the architected concrete components at large-scale. The double-bouligand designs are benchmarked against bouligand and conventional rectilinear counterparts and monolithic casts. In contrast to cast concrete, double-bouligand design demonstrates a non-brittle response and a rising R-curve, due to a hypothesized bilayer crack shielding mechanism. In addition, interlocking behind and crack deflection ahead of the crack tip in bilayer double-bouligand architected concrete elicits a 63% increase in fracture toughness compared to cast counterparts.

The pressure and temperature sensors were outfitted throughout the 1-K platform.Pressure sensors have a range of 0 to 40 bar and temperature sensors had a range of -40°C to 150°C.Temperature sensors are strategically positioned at the pump and nozzle outlets to allow for the monitoring of the material consistency and the operational aspects of the extrusion process.Pressure sensors are positioned at the pump outlet and the nozzle inlet to evaluate changes in baseline extrusion pressure.The presence of entrapped air at the mixing and batching stage can result in temporarily lower pressures owing to the air's compressibility.Slight variations in the material composition may result in pressure inconsistencies.The thixotropic structural build-up from the evolution of the material as a function of residence time in the 1-K pump hopper and hose can result in locally or globally higher pressures.
The temperature sensor fitted at the end of the nozzle tip allows for both an instantaneous indication of the effect of material mixing and extrusion among batches and an overall indication of change in temperature due to the thixotropic structural build-up over time.The continuous monitoring and recording of the material temperature data also acts as an indirect analysis for consistency and operational issues such as potential material clogging or pumping failure due to overheating, thus providing a path for inline troubleshooting.The digital measurements from the pressure and temperature sensors are sent to a processing control user interface (Supplementary Fig. 1e) and displayed in real time on a monitor (Supplementary Fig. 1f).
Buckling failure has been reported to be controlled by a cementitious material's stiffness (shear storage modulus, G' ) in 1-K extrusion processes, while yielding failure in the lower layers has been demonstrated to be correlated with a material's yield stress [1,2].The drawback of the 1-K process is the limited ability to directly control the material composition, rheological properties, and rate of hydration at the nozzle, thus imposing constrains with respect to geometrical fidelity and building rates [1,3,4].On the other hand, the 1-K process provide a facile approach for one-pot extrusion of a varieties of cement-based and alternative binders [5][6][7][8].

Two-Component Additive Manufacturing
Process.The two-component additive process is differentiated from the one-component process as it allows for near real-time tuning of the material's rheological properties through the acceleration or deceleration of hydration at the nozzle [9,10].Unlike a 1-K process that relies on the initial, continuous mixing and pumping of the material in a single stage [1,11], the 2-K process includes a continuous dry powder feedstock followed by mixing and two-stage pumping, and a secondary agitation chamber within the nozzle end-effector featuring an additional inlet for a liquid-phase solution such as a chemical admixture [19,26,64,66].Prior to the extrusion, a setretarder may be mixed into the concrete to either increase the open time of the material or alleviate the required pumping pressure [10].A set-accelerant intermixed immediately prior to extrusion within the nozzle end-effector works to reverse the effect of any upstream retarders from the batch mixing stage as well as rapidly increase the rate of calcium-silicate-hydrate (C-S-H) formation in the concrete [10].The C-S-H nucleation and bridging between cement particles is the primary mechanism for increasing the thixotropy of the material upon addition of the set-accelerant [10,12,13].
The 2-K additive manufacturing process established in this work is depicted in Fig. 2 features an ABB IRB 6700 robot arm (2.85 m reach, 150 kg payload) (Fig. 2a) situated atop an ABB IRBT 6004 track (8.5 m, with 5.7 m linear travel distance) to allow for fabrication of multiple, larger workpieces.The 2-K process leverages a two-stage pump featuring in-situ charging of dry feed and an automated supply of water to continuously mix and convey concrete to the nozzle agitation chamber (Fig. 2b).Below the mixing chamber is located an auger which pumps concrete into a progressive cavity pump that is designed for consistent extrusion of material through the hose.The liquid solution drawn from an accelerant reservoir (Fig. 2c) through a smaller progressive cavity pump feeds into to the 2-K nozzle, injecting setaccelerant into the concrete (Fig. 2d).The concrete and the injected liquid phase entered an agitation chamber within the 2-K nozzle end-effector and intermixed prior to extrusion (Fig. 2e).The agitation chamber and nozzle are mounted on the 6 th axis of the robot arm (using an L-shape coupler).The agitation is achieved by a servo motor rotating a series of interlaced rods at 450 revolutions per minute to ensure homogenization of the concrete and intermixing of the liquid accelerant prior to deposition.
One or more workpieces (Fig. 2f) are positioned in front of the robot track and robot arm with the predefined toolpath for multiple objects.The end-effector is defined relative to local reference frames, termed as the Workobject in RAPID code.Workobjects are commonly defined separately for each executable toolpath.RAPID is the programming language used to control ABB industrial robots.As in the 1-K process, the RAPID code for a toolpath is executable by ABB's Industrial Robot Controller (IRC5) (Fig. 2g).The IRC5 controls all of the dry parameters, such as the end-effector geometry and Workobject local coordinate definitions, and robot movement and speed.An InterProcess Communication (IPC) (Fig. 2h) was used to control all wet parameters related to pumping pressures and flow rates in-situ.
Wet parameters were measured at various locations by sensors and displayed in real-time on a monitor (Fig. 2i) to evaluate the operational performance and material quality.Pressure sensors have a range of 0 to 40 bar, and temperature sensors have a range of -40°C to 150°C.The concrete pump outlet is fitted with a temperature and pressure sensor to observe the material as it is fed into a hose of 25 mm internal diameter.During operation, the pressure and temperature at the concrete pump ranged from 14 to 16 bar and 29°C to 32°C, respectively.Pressure sensors are located at the concrete and accelerant inlets of the agitation chamber to measure the consistent flow prior to intermixing.Lastly, the temperature is measured in the agitation chamber as well as at the nozzle tip immediately prior to extrusion.
During operation, the pressure and temperature of the agitation chamber ranged from 0.4 to 0.7 bar and 32°C to 38°C, respectively.The pressure sensors are particularly critical to providing an instantaneous indication of clogging and overall consistency of the extrusion process.The temperature within the agitation chamber is particularly important for monitoring potential issues such as overheating of material in the agitation chamber due to relatively high energy mixing and addition of set-accelerant.Spikes in either the temperature or pressure in the agitation chamber would be indicative of an operational or processing issues, and can be immediately addressed once observed by the real-time monitoring.These highly instrumented 2-K platform enable informed decision making and can be further enhanced by automating the necessary adjustments in the dry or wet processing parameters based on sensor information [26].Communication between the IRC5 and the IPC was established using an ethernet cable to allow for the concrete and accelerant flow rates to be controlled manually through a human-machine interface (HMI) or digitally through the execution of RAPID code specifying input values for flow rates.Consequently, all fabrication parameters, from concrete and accelerant flow rates to robot path, position, and speed, can be digitally controlled for the fabrication of highly complex, architected materials.Developing communication between often segmented equipment used in additive manufacturing of concrete is necessary in order to improve upon the existing open-loop manufacturing operations that typically lead to trial and error and therefore waste of materials and resources.

Supplementary Note 2: Comparison of One-component (1-K) and Two-Component (2-K) Processes
Supplementary Fig. 2. Additively manufactured structures fabricated using 1-K and 2-K robotic processes, (a) A logo additively manufactured using a 1-K extrusion process (using an IRB 4600) compared to (b) The same toolpath additively manufactured using a 2-K extrusion process (using an IRB 6700), and (c) Several design opportunities including a complex column, non-planar shell, and hexagonal, helicoidal, and Hilbert compliant geometries using the 2-K process.
The 1-K robotic additive manufacturing process is the most prevalent fabrication pathway to date and has been adopted by numerous researchers [14][15][16] and multiple industrial concrete additive manufacturing companies [17].Though widely used, the 1-K process has a limited build-up rate in which the maximum height of a concrete element is constrained by the shear yield strength and stiffness of the extruded material depending on whether the yielding or buckling is the dominate mode of fresh failure [1,[18][19][20].
Both the shear yield strength and shear stiffness gains are governed by the increase in thixotropy, which is directly proportional to the rate of formation of hydration products, specifically the precipitation of C-S-H [10].The 1-K process, depending on the scale, requires slower printing during the manufacturing of the elements to prevent collapse and allow for the build-up to occur or intermittent pauses between fabrication of multiple elements [21], else can become tedious to be utilized as a continuous batching and feeding process.In addition, the intermittent or slower nature of 1-K process in the deposition between layers belabours the fabrication process, thereby potentially exacerbating the effect of cold joints or weak interface between the layers, respectively [21][22][23][24], or introducing additional heterogeneities among the interfaces and filaments.
The 2-K process, on the other hand, aptly addresses these issues by allowing for greater control over the material's rheological properties to increase the shear yield strength and shear stiffness of the material that is necessary for structures more than 0.5 -1 meter tall [19].Moreover, the ability to dose the accelerant greatly improves the geometric quality of the final objects and enables the fabrication of more complex designs (Supplementary Fig. 2b), as compared to the 1-K process (Supplementary Fig. 2a).This, in turn, allows for the execution of intricate material architectures and ambitious purposeful designs (Supplementary Fig. 2c).In addition, the use of a liquid phase solution at the nozzle enabled in the 2-K process can allow for the extra degree of freedom in tuning the material's interfacial and filament chemistry, thus allowing the tuning and functionally grading the mechanical responses.In contrast to the 1-K process, the 2-K process allows for precise and simultaneous control of wet and dry processing parameters.
In both processes, the real-time monitoring and instantaneous communication between the various robotic and pumping equipment can help transition away from open-loop manufacturing operations that often rely on trial and error or one-off procedures.
There are additional challenges in the extrusion-based additive manufacturing of hydraulic suspensions (e.g., cementitious materials), as compared to the more commonplace additive manufacturing of thermoplastics, carbon-fiber reinforced polymers, and other ceramics These may include significant earlyage deformation, partly due to the large size of the printed filaments [25], and reliance on early-stage hydration for hardening [26].For instance, numerous studies have focused on engineering the rheological and hydration properties of additively manufactured cementitious materials to address these challenges [27][28][29][30].
Moreover, one of the major challenges in scaling up additive manufacturing technology is balancing the often large size of the structures with the fabrication rate.Large nozzle sizes have been widely developed to address this issue [31].Previous works have discussed the effect of structure size on early-age deformation and the yield stresses required for a given production rate [32].
Two-component extrusion systems are defined by the ability to accelerate the hydration of cementitious materials at the nozzle tip.This can increase the production rate in the vertical direction in order to achieve large-scale printing [31].In short, for effective scaling up, it is beneficial to use larger filament sizes and a 2K system.This approach not only enhances production rates but also allows for better control over feature sizes (solids or pores) within a reasonable fabrication time.This is particularly advantageous for the mechanical properties and design of mesoscale architectures in civil infrastructure components.A Zeiss X-ray microscope was used to conduct micro-computed tomography (Micro-CT) and map the morphology and distribution of pore phase.A 75 mm wide × 40 mm tall × 40 mm thick, additively manufactured specimen was cut from a lamellar specimen printed at 60 mm/s speed, representative of the printing speed used for the fabrications in this study.The specimen was examined at 0.4x magnification.

Supplementary Note 3: LEFM Analysis of Crack Twisting in
The acquisition was performed with a source power of 140 kV and 10 W. A total of 1601 projections were taken, with one image per rotation angle and a total rotation of 360°.Each projection required a 10 second exposure to maintain an intensity greater than 5000 counts per exposure.The average transmittance was approximately 20% through the thickness and 13% through the width.The source had a working distance of 110 mm and the detector had a working distance of 68 mm relative to the specimen position.The scanning parameters correspond to a resolution of 42 µm.
Binary segmentation was performed on 100 cross-sectional slices taken from the micro-CT specimen at a spacing of 0.25 mm by manual thresholding of grayscale intensities using image processing toolbox of MATLAB 2022 [34].The tangent-slope method was used to evaluate the upper threshold intensity limit of pores, which is determined as the intersection point of the tangents at the initial region of the gray-scale histogram and the upper region of the hydrated product peak.Finally, the pixel label data was obtained from the binary segmented images using MATLAB 2022 [34] to quantify the pore and solid phases.
The interfaces in the architected specimens are predominantly characterized by two main microstructural features: (i) a relatively more porous or less hydrated interfacial region and (ii) a diamond-shaped macroscopic pores at the intersection of 3D-printed filaments leading to the formation of a macro-channel (Supplementary Fig. 4a), both of which can interact with a propagating crack in architected materials.The macroscopic channels (approximately 5 mm wide) were found as a result of the slight filament offset that arose from the alternating nozzle direction along the digitally defined extrusion path (Supplementary Fig. 4b, c) as reported at the 3D-printed cement paste-scale by the authors [35,36].A region of lower degree of hydration (i.e., higher anhydrous cement grains) was frequently observed along the interfaces at the vicinity of the macroscopic channels, shown as brighter horizontal regions (Supplementary Fig. 4b,c,e).This region was hypothesized to be a consequence of the surface drying that occurred during the time gap between printed layers, coupled with higher drying of material at the vicinity of macroscopic channels.These findings are also surprisingly reported in 3D-printed cement paste [35].
The binary segmentation was performed on 100 X-Z cross-sections to quantify the porosity in the specimen (Supplementary Fig. 4g).The contribution to the total porosity is from the diamond-shaped macro-channel and the porosity in the surrounding filament (Supplementary Fig. 4h).The total porosity in the specimen is 7.7 % ± 0.08 %, with 3.0 % ± 0.13 % arising from the presence of the channel.Hence, the channel constitutes approximately 40% of the total porosity in the lamellar specimens.It should be noted that total porosity in lamellar architecture is within the range of 5 -13% porosity reported in the literature for similar nozzle size [37][38][39][40].We hypothesize that this percentage decreases for architected specimens in which the filaments overlap at offset angles, thereby reducing the uniformity of the channel and ultimately reducing the total porosity.The sharp morphology of the diamond-shaped macroscopic pores or channels as observed in Supplementary Fig. 4c,g is conducive to stress concentrations and thus crackflaw interactions.
The macroscopic pores are hypothesized to preferentially deflect the crack path, thus driving the predominant toughening mechanism of crack twisting.Additionally, the stacked formation of voids (Supplementary Fig. 4d) and the higher degree of porosity along the vertical interface between filaments (Supplementary Fig. 4c, f) may contribute to a stabilization of the propagating crack as it twists along filament interfaces.Further investigation of the heterogeneous microstructure may grant additional evidence on the role of weak interfaces on fracture response [41].
Most additive manufacturing processes rely on toolpath algorithms to execute fabrication tasks.Algorithms take user-defined inputs and execute an exact series of operations to produce an output.Toolpath algorithms are used to convert a desired input geometry into a script of code that is executable by the relevant manufacturing technology, such as RAPID for ABB or KRL for KUKA.Most of the script consists of movement instructions that define target coordinates for the robot end-effector to reach before executing the next instruction.The algorithms in this study were developed in Grasshopper, a visual programming interface within Rhinoceros 3D [42].
Complex architectures, for instance functionally graded architectures, require a fabrication process that allows for the instantaneous adjustment of filament dimensions.These dimensions are most efficiently controlled by varying the nozzle speed between each Target point (Supplementary Fig. 5f-i).The instantaneous nozzle speed (Supplementary Fig. 5f-ii) is calculated by multiplying a user-defined mathematical function for the desired functional grading if needed (Supplementary Fig. 5f-ii) with the user-defined nozzle speed (Supplementary Fig. 5a-v) to control the total volume extruded between two Targets.The same mathematical function can also be used to scale the z-coordinate of the polyline points to meet the desired layer height.Once computed, the instantaneous speeds and cartesian coordinates of each point can be formatted (Supplementary Fig. 5f-iv) as Move instructions for an entire toolpath.The robot instructions for a specific toolpath comprise a Procedure in the RAPID program, which is included within a Module along with the relevant global definitions of end-effectors and Workobjects.
The architecture-specific algorithm is agnostic to any individual robot's movement capabilities.Hence, the robot path is simulated in a virtual environment within software (RobotStudio) as a dry-run to assess for any compilation errors as well as any movement errors, such as collisions, physically unreachable points, or other singularity issues due to a current position of the joints.Individual Modules are then called in the 'main' Program file, and the entire RAPID Program inclusive of main and the respective toolpath Modules is uploaded to the IRC5 Teach Pendant.Specific toolpath Procedures can be executed individually, or as a series of consecutive prints by executing main.Once uploaded, the robotic platform is equipped to execute toolpaths to fabricate complex bio-inspired cementitious architected materials.
Where for load-line displacement,   is equal to 1.9,  0 denotes the initial crack tip extension equivalent to the notch length, and   was computed as the area under the force-displacement curve past the peak load of the specimen: The fracture toughness,   , can then be computed as follows [61,62]: The   curve (Fig. 3d) was computed for incremental points of crack extension,   , based on the instantaneous specimen compliance,   .Compliance was evaluated as the instantaneous ratio of crosshead displacement to applied load [63]: Where   represents the instantaneous crosshead displacement for measurement n, and   represents the instantaneous load.Both crosshead and load measurements are taken at a frequency of 10 Hz.The instantaneous crack tip extension,   , was subsequently calculated as the following relationship [63]: As the crack tip extends, the   increases and the evolution of   can be plotted against crack extension   as resistance curve (R-curve).The R-curve is a commonly used for understanding the fracture toughness of a material and is advantageous for concurrently investigating the material's toughness crack initiation (  ) and crack propagation (  ).The R-curves are plotted past the maximum crack extension of   = 0.25( −   ) specified by ASTM E1820-20b (Fig. 3d) and are considered for the calculation of the J-integral [55].For specimens exhibiting a post-peak softening, the toughness is measured for a crack extension corresponding to 1% of the respective specimen's peak load.
Calculation of Work of Fracture.The work of fracture represents the total energy required to generate a unit fracture area and was calculated as the total area under the load-displacement curve divided by two times the fractured surface area [43]: Where   represents the instantaneous measured load and   represents the corresponding instantaneous measured displacement.

Bouligand Architecture Supplementary Fig. 3 .. 4 .
(a) Cross-sectional view of bouligand fractured plane highlighting the idealized fractured plane, (b) Schematic representation of idealized fractured plane and mathematical definition of rotated cartesian axes x', y', z', twist angle, , kink angle, , (c) Idealized fractured path projected on Z-X surface, and (d) Ratio between energy release rate of propagating crack,   , and the energy release rate of a linear elastic material under Mode-I fracture,   [33].(a) Representative lamellar architecture and two dimensional cross-sectional views of the layered additively manufactured filament obtained from micro-CT, (b,c) the X-Z plane highlighting the diamond-shaped macroscopic pores and interfacial regions of locally higher anhydrous cement, (d,e) Y-Z plane highlighting regions of macroscopic pores and regions of locally higher anhydrous cement, (f) the X-Y plane highlighting the interfacial regions of locally higher porosity between adjacent filaments in the same layer.(g) A binary segmentation of the X-Z plane of the micro-CT specimen, (h) Porosity distribution obtained from the binary segmentation differentiating the total porosity contribution from the diamond-shaped macroscopic pores from surrounding filament porosity and the total porosity.